Evaluate:
`int_(0)^(pi//2)sinxdx`

Explanation

To evaluate the integral \( I = \int_{0}^{\frac{\pi}{2}} \sin x \, dx \), we can follow these steps:

### Step 1: Set up the integral
We start by defining the integral we want to evaluate:
\[ I = \int_{0}^{\frac{\pi}{2}} \sin x \, dx \]

### Step 2: Find the antiderivative of \(\sin x\)
The next step is to find the antiderivative of \(\sin x\). We know that:
\[ \int \sin x \, dx = -\cos x + C \]
where \(C\) is the constant of integration.

### Step 3: Apply the limits of integration
Now we will apply the limits of integration from \(0\) to \(\frac{\pi}{2}\):
\[ I = \left[-\cos x\right]_{0}^{\frac{\pi}{2}} \]

### Step 4: Evaluate at the upper limit
First, we evaluate at the upper limit \(x = \frac{\pi}{2}\):
\[ -\cos\left(\frac{\pi}{2}\right) = -0 = 0 \]

### Step 5: Evaluate at the lower limit
Next, we evaluate at the lower limit \(x = 0\):
\[ -\cos(0) = -1 \]

### Step 6: Subtract the results
Now we subtract the value at the lower limit from the value at the upper limit:
\[ I = 0 - (-1) = 0 + 1 = 1 \]

### Final Result
Thus, the value of the integral is:
\[ I = 1 \]

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